The Substitution of Similars: The True Principle of Reasoning, Derived from a Modification of Aristotle's Dictum |
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... AXIOMS OF EQUALITY GENERAL FORMULA OF MATHEMATICAL INFERENCE INFERENCE BY INEQUALITIES . SUBSTITUTION OF EQUALS OR SIMILARS PAGE I 4 5 7 9 II 15 · 19 20 23 GENERAL FORMULA OF LOGICAL INFERENCE 24 EXAMPLES OF LOGICAL SUBSTITUTION . 25 ...
... AXIOMS OF EQUALITY GENERAL FORMULA OF MATHEMATICAL INFERENCE INFERENCE BY INEQUALITIES . SUBSTITUTION OF EQUALS OR SIMILARS PAGE I 4 5 7 9 II 15 · 19 20 23 GENERAL FORMULA OF LOGICAL INFERENCE 24 EXAMPLES OF LOGICAL SUBSTITUTION . 25 ...
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... axiom was perfectly adapted to this view . The so - called Dictum de omni is , in Latin phrase , as follows- Quicquid de omni valet , valet etiam de quibusdam et singulis . And the corresponding Dictum de nullo is similarly- Quicquid de ...
... axiom was perfectly adapted to this view . The so - called Dictum de omni is , in Latin phrase , as follows- Quicquid de omni valet , valet etiam de quibusdam et singulis . And the corresponding Dictum de nullo is similarly- Quicquid de ...
Page 15
... axiom of quantity ; and the force of the axiom may best be illustrated in the first place by looking at it in its mathematical aspect . 15. The axiom indeed with which Euclid begins to build presents at first sight little or no resem ...
... axiom of quantity ; and the force of the axiom may best be illustrated in the first place by looking at it in its mathematical aspect . 15. The axiom indeed with which Euclid begins to build presents at first sight little or no resem ...
Page 16
... axiom asserts that Things equal to the same thing are equal to each other . In symbols , a = b = c gives a = c . Here two equations are apparently necessary in order that an inference may be evolved ; and there is something peculiar ...
... axiom asserts that Things equal to the same thing are equal to each other . In symbols , a = b = c gives a = c . Here two equations are apparently necessary in order that an inference may be evolved ; and there is something peculiar ...
Page 17
... axiom of Euclid thus requires to be supplemented by two other axioms , which can only be expressed in somewhat awkward language , as follows : — If the first of three things be equal to the second , but the second be unequal to the ...
... axiom of Euclid thus requires to be supplemented by two other axioms , which can only be expressed in somewhat awkward language , as follows : — If the first of three things be equal to the second , but the second be unequal to the ...
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Common terms and phrases
A B C D abacus ABCD adjective affirmative proposition Algebra analogy Aristotle Aristotle's dictum assert axiom axiom of Euclid Boole Boole's BROOKE FOSS WESTCOTT calculus Cambridge canon cloth conclusion copula Crown 8vo differs Edward Thring ELEMENTARY TREATISE English equal equal-sided equivalent Euclid example expression Extra fcap fallacy Fcap follows form of inference forms of reasoning formula George Bentham Grammar Greek hence identity illustrated indefinite indirect inequalities infallible Iron J. S. Mill John's College late Fellow law of duality laws of thought ledge logicians means ments metals are elements method monarch negative proposition obtain ordinary oxygen planet pound weight premises PRINCIPLE OF REASONING principle of substitution proposition or equation quantification quantity reader REESE LIBRARY relation represented Schools Second Edition second member self-evident self-luminous slips substitution of similars syllogism symbols thing Third Edition tion triangle truth undecomposable substance
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